Hodge Conjecture

Conjecture

It is conjectured that:

For projective algebraic varieties, Hodge cycles are rational linear combinations of algebraic cycles.


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Source of Name

This entry was named for William Vallance Douglas Hodge.


Sources

  • 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Millennium Prize problems
  • 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Millennium Prize problems
  • 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Appendix $18$: Millennium Prize problems: $2$.
  • 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): Appendix $23$: Millennium Prize problems: $2$.
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